Average Error: 20.4 → 0.2
Time: 5.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.5426885262265421 \cdot 10^{29} \lor \neg \left(z \le 190386035.853135854\right):\\ \;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.5426885262265421 \cdot 10^{29} \lor \neg \left(z \le 190386035.853135854\right):\\
\;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\\

\end{array}
double f(double x, double y, double z) {
        double r344289 = x;
        double r344290 = y;
        double r344291 = z;
        double r344292 = 0.0692910599291889;
        double r344293 = r344291 * r344292;
        double r344294 = 0.4917317610505968;
        double r344295 = r344293 + r344294;
        double r344296 = r344295 * r344291;
        double r344297 = 0.279195317918525;
        double r344298 = r344296 + r344297;
        double r344299 = r344290 * r344298;
        double r344300 = 6.012459259764103;
        double r344301 = r344291 + r344300;
        double r344302 = r344301 * r344291;
        double r344303 = 3.350343815022304;
        double r344304 = r344302 + r344303;
        double r344305 = r344299 / r344304;
        double r344306 = r344289 + r344305;
        return r344306;
}
↓
double f(double x, double y, double z) {
        double r344307 = z;
        double r344308 = -5.542688526226542e+29;
        bool r344309 = r344307 <= r344308;
        double r344310 = 190386035.85313585;
        bool r344311 = r344307 <= r344310;
        double r344312 = !r344311;
        bool r344313 = r344309 || r344312;
        double r344314 = x;
        double r344315 = 0.07512208616047561;
        double r344316 = y;
        double r344317 = r344316 / r344307;
        double r344318 = r344315 * r344317;
        double r344319 = 0.0692910599291889;
        double r344320 = r344319 * r344316;
        double r344321 = r344318 + r344320;
        double r344322 = r344314 + r344321;
        double r344323 = 6.012459259764103;
        double r344324 = r344307 + r344323;
        double r344325 = r344324 * r344307;
        double r344326 = 3.350343815022304;
        double r344327 = r344325 + r344326;
        double r344328 = sqrt(r344327);
        double r344329 = r344316 / r344328;
        double r344330 = r344307 * r344319;
        double r344331 = 0.4917317610505968;
        double r344332 = r344330 + r344331;
        double r344333 = r344332 * r344307;
        double r344334 = 0.279195317918525;
        double r344335 = r344333 + r344334;
        double r344336 = r344335 / r344328;
        double r344337 = r344329 * r344336;
        double r344338 = r344314 + r344337;
        double r344339 = r344313 ? r344322 : r344338;
        return r344339;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.4
Target0.2
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737680000:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)\right) \cdot \frac{1}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.542688526226542e+29 or 190386035.85313585 < z

    1. Initial program 43.0

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)}\]

    if -5.542688526226542e+29 < z < 190386035.85313585

    1. Initial program 0.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt0.7

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394} \cdot \sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}}\]

    4. Applied times-frac0.3

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.5426885262265421 \cdot 10^{29} \lor \neg \left(z \le 190386035.853135854\right):\\ \;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\sqrt{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 657611897278737680000) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))